Question

Qual e a derivada t= t^3+k
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t

Answer 1

Resolução da questão, veja:

Calcular a derivada da função t³ + k/t, vejamos:

Aplicando a propriedade do derivado para o quociente ((u/v)' = (v(u)'-(v)'u)/(v^2))) teremos que:

$\mathsf{\dfrac{d}{dt}\bigg(\dfrac{t^{3}+k}{t}\bigg)}}}\\\\\\\\\\ \mathsf{\dfrac{t\dfrac{d}{dt}(t^{3}+k)-\dfrac{d}{dt}(t)(t^{3}+k)}{t^{2}}}}}}}}}}}\\\\\\\\\\ \mathsf{\dfrac{-1(t^{3}+k)+t\bigg(\dfrac{d}{dt}(t^{3})+\dfrac{d}{dt}(k)\bigg)}{t^{2}}}}}}}\\\\\\\\\\ \mathsf{\dfrac{-(t^{3}+k)+t(3t^{3-1}+0)}{t^{2}}}}\\\\\\\\\\ \mathsf{\dfrac{-t^{3}+t^{3}~\cdot~3-k}{t^{2}}}}\\\\\\\\\\ \mathsf{\dfrac{3t^{3}-t^{3}-k}{t^{2}}}}\\\\\\\\\\ \large\boxed{\boxed{\boxed{\boxed{\boxed{\mathsf{\dfrac{2t^{3}-k}{t^{2}}}}}}}}}}}}}}}}}}}}}}}}}}}$

Ou seja, o derivado da função t³ + k/t é igual a 2t³ - k/t².

Espero que te ajude. '-'